The 3rd Generation Partnership Project (3GPP) is responsible for the standardization of the Universal Mobile Telecommunication System (UMTS) and Long Term Evolution (LTE). The 3GPP work on LTE is also referred to as Evolved Universal Terrestrial Access Network (E-UTRAN). LTE is a technology for realizing high-speed packet-based communication that can reach high data rates both in the downlink and in the uplink, and is thought of as a next generation mobile communication system relative to UMTS. In order to support high data rates, LTE allows for a system bandwidth of 20 MHz, or up to 100 MHz when carrier aggregation is employed. LTE is also able to operate in different frequency bands and can operate in at least Frequency Division Duplex (FDD) and Time Division Duplex (TDD) modes.
LTE uses Orthogonal Frequency-Division Multiplexing (OFDM) in the downlink and Discrete-Fourier-Transform-spread (DFT-spread) OFDM in the uplink. The basic LTE downlink physical resource can thus be seen as a time-frequency grid as illustrated in FIG. 1, where each resource element corresponds to one OFDM subcarrier during one OFDM symbol interval.
In the time domain, LTE downlink transmissions are organized into radio frames of 10 milliseconds, as shown in FIG. 2, with each radio frame consisting of ten equally-sized subframes of length Tsubframe=1 millisecond. For normal cyclic prefix, one subframe consists of fourteen OFDM symbols. The duration of each OFDM symbol is approximately 71.4 microseconds (μs).
Furthermore, the resource allocation in LTE is typically described in terms of resource blocks, where a resource block corresponds to one slot (0.5 ms) in the time domain and twelve contiguous subcarriers in the frequency domain. A pair of two adjacent resource blocks in time direction (1.0 ms) is known as a resource block pair. Resource blocks are numbered in the frequency domain, starting with 0 from one end of the system bandwidth.
Downlink transmissions are dynamically scheduled, i.e., in each subframe the base station transmits control information about to which terminals data is transmitted and within which resource blocks the data is transmitted, in the current downlink subframe. This control signaling (PDCCH) is typically transmitted in the first one, two, three, or four OFDM symbols in each subframe and the number n=1, 2, 3 or 4 is known as the Control Format Indicator (CFI). The downlink subframe also contains common reference symbols, which are known to the receiver and used for coherent demodulation of the control information, for example. A portion of a downlink subframe with CFI=3 OFDM symbols as control is illustrated in FIG. 3.
From Release 11 of the 3GPP specifications for LTE (LTE Rel-11) onwards, the above described resource assignments can be scheduled on the Enhanced Physical Downlink Control Channel (EPDCCH) as well as on the Physical Downlink Control Channel (PDCCH). For Rel-8 LTE to Rel-10 LTE, only the PDCCH is used for this purpose.
The reference symbols shown in FIG. 3 are the cell-specific reference symbols (CRS) and are used to support multiple functions including fine time and frequency synchronization and channel estimation for certain transmission modes.
In a cellular communication system there is a need to measure the channel conditions, in order to know what transmission parameters to use. These parameters include, e.g., modulation type, coding rate, transmission rank, and frequency allocation. This applies to uplink (UL) as well as downlink (DL) transmissions.
The scheduler that makes the decisions on the transmission parameters is typically located in the base station (referred to in 3GPP documentation as an “eNB”). Hence, it can measure channel properties of the UL directly using known reference signals that the terminals (referred to in 3GPP documentation as “user equipment” or “UEs”) transmit. These measurements then form a basis for the UL scheduling decisions that the eNB makes, which are then sent to the UEs via a downlink control channel.
Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is particularly improved if both the transmitter and the receiver are equipped with multiple antennas, which results in a multiple-input multiple-output (MIMO) communication channel. Such systems and/or related techniques are commonly referred to as MIMO.
The LTE standard is currently evolving to include enhanced MIMO support. A core component in LTE is the support of MIMO antenna deployments and MIMO related techniques. Currently, LTE-Advanced supports an 8-layer spatial multiplexing mode for eight transmit (Tx) antennas, with channel dependent precoding. The spatial multiplexing mode is aimed for high data rates in favorable channel conditions. An illustration of the transmission structure for precoded spatial-multiplexing operation is provided in FIG. 4.
As seen in FIG. 4, the information carrying symbol vectors is multiplied by an NT×r precoder matrix W, which serves to distribute the transmit energy in a subspace of the NT-dimensional vector space, where NT is the number of transmitting antenna ports. The precoder matrix is typically selected from a codebook of possible precoder matrices, and typically indicated by means of a precoder matrix indicator (PMI), which specifies a unique precoder matrix in the codebook for a given number of symbol streams. The r symbols in s each correspond to a layer, and r is referred to as the transmission rank. In this way, spatial multiplexing is achieved, since multiple symbols can be transmitted simultaneously over the same time/frequency resource element (TFRE). The number of symbols r is typically adapted to suit the current channel properties.
As noted above, LTE uses OFDM in the downlink (and DFT-precoded OFDM in the uplink), and hence the received NR×1 vector yn for a certain TFRE on subcarrier n (or alternatively data TFRE number n) is modeled by:yn=HnWsn+en,where NR is the number of receiver antenna ports and en is a noise/interference vector obtained as realizations of a random process. The precoder W can be a wideband precoder, which is constant over frequency, or frequency selective.
The precoder matrix is often chosen to match the characteristics of the NR×NT MIMO channel matrix Hn, resulting in so-called channel-dependent precoding. This is also commonly referred to as closed-loop precoding, and essentially strives to focus the transmit energy into a subspace that is strong, in the sense of conveying much of the transmitted energy to the UE. In addition, the precoder matrix may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the UE, the inter-layer interference is reduced.
The transmission rank, and thus the number of spatially multiplexed layers, is reflected in the number of columns of the precoder. For efficient performance, it is important that a transmission rank that matches the channel properties is selected.
In LTE Release-10, a new reference symbol sequence or reference signal, referred to as CSI-RS, was introduced for purposes of estimating channel state information (CSI). The CSI-RS provides several advantages over basing CSI feedback on the common or cell-specific reference symbols (CRS) which were used for that purpose in previous releases. Firstly, the CSI-RS is not used for demodulation of the data signal, and thus does not require the same density, i.e., the overhead of the CSI-RS is substantially less than that of the CRS. Secondly, CSI-RS provides a much more flexible means to configure CSI feedback measurements (e.g., which CSI-RS resource to measure on can be configured in a UE specific manner).
By measuring on a CSI-RS, a UE can estimate the effective channel the CSI-RS is traversing, where the effective channel includes the radio propagation channel and antenna gains. In more mathematical rigor this implies that if a known CSI-RS signal x is transmitted, a UE can estimate the coupling between the transmitted signal and the received signal, i.e., the effective channel. Hence, if no virtualization is performed in the transmission, the received signal y can be expressed as:y=Hx+e and the UE can estimate the effective channel H.
Up to eight CSI-RS ports can be configured for a Rel-11 UE, which means that the UE can thus estimate the channel from up to eight transmit antennas.
For CSI feedback, LTE has adopted an implicit CSI mechanism where a UE does not explicitly report, e.g., the complex-valued elements of a measured effective channel, but rather the UE recommends a transmission configuration for the measured effective channel. The recommended transmission configuration thus implicitly gives information about the underlying channel state.
In LTE, CSI feedback is given in terms of a transmission rank indicator (RI), a precoder matrix indicator (PMI), and one or two channel quality indicator(s) (CQI). The CQI/RI/PMI report can be wideband or frequency selective, depending on which reporting mode is configured.
The RI corresponds to a recommended number of streams that are to be spatially multiplexed and thus transmitted in parallel over the effective channel. The PMI identifies a recommended precoding matrix codeword (in a codebook which contains precoders with the same number of rows as the number of CSI-RS ports) for the transmission, which relates to the spatial characteristics of the effective channel. The CQI represents a recommended transport block size, i.e., code rate, and LTE supports transmission of one or two simultaneous transmissions of transport blocks on each of up to four different layers, i.e., separately encoded blocks of information, to a UE in a subframe. There is thus a relation between a CQI and an SINR of the spatial stream(s) over which the transport block or blocks are transmitted.
Recent development in 3GPP has led to the discussion of two-dimensional antenna arrays where each antenna element has an independent phase and amplitude control, thereby enabling beamforming in both in the vertical and the horizontal dimensions. Such antenna arrays may be (partly) described by the number of antenna columns corresponding to the horizontal dimension Nh, the number of antenna rows corresponding to the vertical dimension Nv, and the number of dimensions corresponding to different polarizations Np. The total number of antennas is thus N=NhNvNp. An example of an antenna array where Nh=4 and Nv=8 is illustrated in FIG. 5. This array furthermore consists of cross-polarized antenna elements, meaning that Np=2. We will denote such an antenna as an 8×4 antenna array with cross-polarized antenna elements. Note that the right-hand side of FIG. 5 shows an example antenna port layout corresponding to the same antenna array, with 2 vertical ports and 4 horizontal ports. This could be obtained, for instance, by virtualizing each port with 4 vertical antenna elements, i.e., mapping outputs from 4 vertical antenna elements to each of the ports shown on the right-hand side of FIG. 5. Hence, assuming cross-polarized ports are present, the UE can measure CSI-RS for 16 antenna ports, in this example.
Precoding may be interpreted as multiplying the signal with different beamforming weights for each antenna port prior to transmission. A typical approach is to tailor the precoder to the antenna form factor, i.e., taking into account N1, N2 and Np when designing the precoder codebook.
A common approach when designing precoder codebooks tailored for two-dimensional antenna arrays is to combine precoders tailored for a horizontal array and a vertical array of antenna ports, respectively, by means of a Kronecker product. A precoding matrix W in the codebook is then represented as:W=W1W2,  (Eq. 1)where W1 is defined as:
                                          W            1                    =                      (                                                                                                      X                      1                                        ⊗                                          X                      2                                                                                        0                                                                              0                                                                                            X                      1                                        ⊗                                          X                      2                                                                                            )                          ,                            (                  Eq          .                                          ⁢          2                )            
wherein:                X1 is a N1×L1 matrix (corresponding to a beam group) with L1 column vectors which are constructed using O1 times oversampled Discrete-Fourier-Transform (DFT) vectors vl of length        
                    N        1            ⁢              :            ⁢                          ⁢              v        l              =                  [                                            1                                                      e                                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                    l                                                                              N                      1                                        ⁢                                          O                      1                                                                                                          …                                                      e                                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ⁡                                              (                                                                              N                            1                                                    -                          1                                                )                                                              ⁢                    l                                                                              N                      1                                        ⁢                                          O                      1                                                                                                          ]            T        ;                X2 is a N2×L2 matrix (corresponding to a beam group) with L2 column vectors which are constructed using O2 times oversampled DFT vectors ul of length        
                    N        2            ⁢              :            ⁢                          ⁢              u        l              =                  [                                            1                                                      e                                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                    π                    ⁢                                                                                  ⁢                    l                                                                              N                      2                                        ⁢                                          O                      2                                                                                                          …                                                      e                                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ⁡                                              (                                                                              N                            2                                                    -                          1                                                )                                                              ⁢                    l                                                                              N                      2                                        ⁢                                          O                      2                                                                                                          ]            T        ;                N1 and N2 are the numbers of antenna ports per polarization in a first dimension (e.g., horizontal) and in a second dimension (e.g., vertical), respectively;        L1 and L2 are referred to as the beam group sizes of the first and second dimensions, respectively; and        [ ]T denotes the transpose operation.        
The matrix W2 in Eq. 1 selects beams from these beam groups (in the two dimensions). W2 may operate per subband, to enable fast beam selection (per subband) across the system bandwidth.
In Rel-13 LTE, class A CSI reporting refers to the case where the UE reports CSI using non-precoded CSI reference symbols or signals in both the first and second dimensions. In Rel-13, parameterized codebooks for 12 and 16 ports are supported, in addition to a two-dimensional 8-port codebook. The Rel-13 class A codebook is configured with five Radio Resource Control (RRC) configured parameters:                The numbers N1, N2 of antenna ports per polarization in each dimension; N1, N2∈{1,2,3,4,8}, where the valid candidates are (N1, N2)=(8,1), (2,2), (2,3), (3,2), (2,4), (4,2)        The oversampling factors O1, O2 in each dimension; For each (N1, N2), configurability of (O1, O2) is restricted to two possible fixed pairs as given below:        
(N1, N2)(O1, O2) combinations(8, 1)(4, —), (8, —)(2, 2)(4, 4), (8, 8)(2, 3){(8, 4), (8, 8)}(3, 2){(8, 4), (4, 4)}(2, 4){(8, 4), (8, 8)}(4, 2){(8, 4), (4, 4)}                A configuration parameter Config that can take on values of 1, 2, 3, or 4.        
It should be noted that for the case(s) where one dimension has a single port, the oversampling factor (for that dimension), and Config values of 2 and 3 do not apply.
Rank-1 Class A Codebook
Given the set of values N1, N2, O1, and O2, the W1 matrices in Eq. 1 and Eq. 2 are constructed with:
                              (                                    L              2              ′                        ,                          L              2              ′                                )                =                  {                                                                                                                (                                              4                        ,                        2                                            )                                        ,                                                                                                              if                      ⁢                                                                                          ⁢                                              N                        1                                                              ≥                                          N                      2                                                                                                                                                              (                                              2                        ,                        4                                            )                                        ,                                                                                                              else                      ⁢                                                                                          ⁢                                              N                        1                                                              <                                          N                      2                                                                                            ,                                              (                  Eq          .                                          ⁢          3                )            where L′1 and L′2 are the number of columns in X1 and X2, respectively. The values of L′1 and L′2 are first chosen such that L′1>L1 and L′2>L2, to form an extended codebook. Depending on the value of Config, a subset of codewords from the extended codebook is selected as an active subset, i.e. used in CSI feedback, as follows:
      Config    =                  1        ⁢                  :                ⁢                                  ⁢                  (                                    L              1                        ,                          L              2                                )                    =              (                  1          ,          1                )                  Config    =                  2        ⁢                  :                ⁢                                  ⁢                  (                                    L              1                        ,                          L              2                                )                    =                        (                      2            ,            2                    )                ⁢                                  [        square        ]                  Config    =                  3        ⁢                  :                ⁢                                  ⁢                  (                                    L              1                        ,                          L              2                                )                    =                        (                      2            ,            2                    )                ⁢                                  [                  non          ⁢                      -                    ⁢          adjacent          ⁢                                          ⁢          two          ⁢                      -                    ⁢          dimensional          ⁢                                          ⁢                      beams            /            checkerboard                          ]                  Config    =                  4        ⁢                  :                ⁢                                  ⁢                  (                                    L              1                        ,                          L              2                                )                    =              {                                                                              (                                      4                    ,                    1                                    )                                ,                                                                                      if                  ⁢                                                                          ⁢                                      N                    1                                                  ≥                                  N                  2                                                                                                                          (                                      1                    ,                    4                                    )                                ,                                                                                      else                  ⁢                                                                          ⁢                                      N                    1                                                  <                                  N                  2                                                                        Hence, config 2-4 contains four beams per beam group while config 1 only contains a single beam per beam group. Let i1,1=0, 1, . . . , O1N1/s1−1 and i1,2=0, 1, . . . , O2N2/s2−1 denote the first PMI index in dimension 1 and 2, respectively. Here, s1 and s2 represent beam group spacing, or how far apart the beam groups can be in angle, in dimension 1 and 2, respectively. From the active subset of codewords described above, the UE selects one codeword and reports this selection via a second PMI i′2 in aperiodic reporting on PUSCH. Hence, the rank-1 codebook can be defined in terms of i1,1, ii,2, and i′2 as shown in the table illustrated in FIG. 15, which shows a Rank-1 Class A Codebook for N1≥N2.
In FIG. 15, each rank-1 codeword Wm1,m2,n(1) is defined as
                                          W                                          m                1                            ,                              m                2                            ,              n                                      (              1              )                                =                                    1                              Q                                      ⁡                          [                                                                                                                  v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                                                        φ                        n                                            ⁢                                                                        v                                                      m                            1                                                                          ⊗                                                  u                                                      m                            2                                                                                                                                                          ]                                      ,                            (                  Eq          .                                          ⁢          4                )            wherein φn=ejπn/2. In Eq. 4, the single layer of data is transmitted on the two-dimensional beam involving the m1th beam in the first dimension and the m2th beam in the second dimension, where:
                              v                      m            1                          =                  [                                                    1                                                              e                                      j                    ⁢                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  m                          1                                                                                                                      O                          1                                                ⁢                                                  N                          1                                                                                                                                                …                                                                                                                                e                                                                              j                            ⁢                                                                                          2                                ⁢                                π                                ⁢                                                                                                                                  ⁢                                                                                                      m                                    1                                                                    ⁡                                                                      (                                                                                                                  N                                        1                                                                            -                                      1                                                                        )                                                                                                  ⁢                                l                                                                                                                              O                                  1                                                                ⁢                                                                  N                                  1                                                                                                                                              ⁢                                                                                                                                                    ]                                        T                                    ,                                                                                        (                  Eq          .                                          ⁢          5                )                                          u                      m            2                          =                  [                                                                      1                                                                      e                                          j                      ⁢                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      m                            2                                                                                                                                O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                …                                                                                                                                              e                                                                                    j                              ⁢                                                                                                2                                  ⁢                                  π                                  ⁢                                                                                                                                          ⁢                                                                                                            m                                      2                                                                        ⁡                                                                          (                                                                                                                        N                                          2                                                                                -                                        1                                                                            )                                                                                                        ⁢                                  l                                                                                                                                      O                                    2                                                                    ⁢                                                                      N                                    2                                                                                                                                                        ⁢                                                                                                                                                                ]                                            T                                        ,                                                                        .                                              (                  Eq          .                                          ⁢          6                )            and where the superscript T indicates matrix transpose.
For each Config value, the different possible values of i′2 and the associated values of s1 and s2 are given in the table shown in FIG. 16, which shows the election of i′2 and (s1, s2) for Rank-1 Class A Codebook.
This codebook can be interpreted as follows: The left column in the table shown in FIG. 16 describes how the beams in the beam group are distributed across the first and second dimension. The indices i1,1 and i1,2 in in the table shown in FIG. 15 are wideband, and used to select the beams in the beam group. The index i′2 is used to perform beam selection within the beam group (as selected by i1,1 and i1,2) and co-phasing of the beams in the different polarizations. The parameters s1 and s2 indicate the shift between different beam groups. For instance, the table shown in FIG. 15 shows that given i1,1, the indices for the first dimension are s1 i1,1, s1 i1,1+1, s1 i1,1+2, s1 i1,1+3, while the table shown in FIG. 16 shows that for Config 2, only i′2 indices (0-7,16-23) can be selected, hence only s1 i1,1, s1 i1,1+1 can be selected for this configuration. Effectively, the beam group size of the first dimension in Config 2 is two, i.e. L1=2.
Rank-2 Class A Codebook
Given the set of values N1, N2, O1, and O2, the W1 matrices in Eqs. 1 and 2 are constructed in the same manner described above (i.e., using the same values of (L′1, L′2) defined in Eq. 3). The rank-2 codebook can be defined in terms of i1,1, i1,2, and i′2 as shown in the table shown in FIG. 17. In the table shown in FIG. 17, each rank-2 codeword Wm1,m2,m1′,m2′,n(2) is defined as
                                          W                                          m                1                            ,                              m                2                            ,                              m                1                ′                            ,                              m                2                ′                            ,              n                                      (              2              )                                =                                    1                                                2                  ⁢                                                                          ⁢                  Q                                                      ⁡                          [                                                                                                                  v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        v                                                  m                          1                          ′                                                                    ⊗                                              u                                                  m                          2                          ′                                                                                                                                                                                                        φ                        n                                            ⁢                                                                        v                                                      m                            1                                                                          ⊗                                                  u                                                      m                            2                                                                                                                                                                                                  -                                                  φ                          n                                                                    ⁢                                                                        v                                                      m                            1                            ′                                                                          ⊗                                                  u                                                      m                            2                            ′                                                                                                                                                          ]                                      ,                            (                  Eq          .                                          ⁢          7                )            wherein φn=ejπn/2. In Eq. 7, the first layer of data is transmitted on the two-dimensional beam involving the m1th beam in the first dimension and the m2th beam in the second dimension; the second layer of data is transmitted on the two-dimensional beam involving the (m1′)th beam in the first dimension and the (m2′)th beam in the second dimension. Furthermore, i1,1, i1,2, and the beam offsets p1, and p2 in the table shown in FIG. 17, which illustrates a Rank 2 Class A Codebook, are defined as:                i1,1=0, 1, . . . , O1N1/s1−1        i1,2=0, 1, . . . , O2N2/s2−1        p1=1 and p2=1.        
For each Config value, the different possible values of i′2 and the associated values of s1 and s2 corresponding to the rank-2 Class A codebook are given in the table shown in FIG. 18.
In the table shown in FIG. 18, which shows selection of i′2 and (s1, s2) for Rank 2 Class A Codebook, two-dimensional beams are indicated by square shaped boxes. A square box with indices a′b′ in the first dimension (e.g., horizontal) and indices c′d′ in the second dimension (e.g., vertical) corresponds to any codeword from the table shown in FIG. 18 that satisfies the conditions m1=s1i1,1+a′, m2=s2i1,2+c′, m′1=s1i1,1+b′, and m′2=s2i1,2+d′. For each Config value, the shaded, dashed and crossed boxes represent the two-dimensional beams that can be used to form the active subset of codewords from the extended codebook table.
Rank-3 Class A Codebook
The rank-3 codebook can be defined in terms of four parameters: i1,1, i1,2, k and i′2. The different parameter values of parameter k represent different orthogonal beam groups. Each beam group consists of L′1 beams in the first dimension and L′2 beams in the second dimension where (L′1,L′2) are defined in Eq. 3. During feedback, the UE feeds back k as part of the W1 indication. Each k value corresponds to one pair of (δ1,δ2) parameters as shown in Table 1. There can be two alternatives for the maximum value of k:                Alt 1. Two values: k=0,1 in Table 1        Alt 2. Maximum eight values:                    If N1>1 and N2>1: k=0, 1, 2 . . . , 7 in Table 1            If N2=1:k=0, 1, 2 Table 1                        
TABLE 1Mapping between k and (δ1, δ2)kδ01234567If N1 > 1 andδ1O10O12O10O12O12O1N2 > 1δ20O2O202O22O2O22O2If N2 = 1δ1O12O13O1δ2000
Furthermore, i1,1 and i1,2, are defined as:                i1,1=0, 1, . . . , O1N1/s1−1        i1,2=0, 1, . . . , O2N2/s2−1.        
Then, the rank-3 codebook can be defined as shown in the table shown in FIG. 19, which shows a Rank 3 Class A Codebook. In the table shown in FIG. 19, the rank-3 codewords Wm1,m1′,m2m2′(3) and {tilde over (W)}m1,m1′,m2m2′(3) indexed by i′2 are defined as:
                                          W                                          m                1                            ,                              m                1                ′                            ,                              m                2                            ,                              m                2                ′                                                    (              3              )                                =                                    1                                                3                  ⁢                                                                          ⁢                  Q                                                      ⁡                          [                                                                                                                  v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        v                                                  m                          1                          ′                                                                    ⊗                                              u                                                  m                          2                          ′                                                                                                                                                                                                        v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        -                                                  v                                                      m                            1                                                                                              ⊗                                              u                                                  m                          2                                                                                                                                                                        -                                                  v                                                      m                            1                            ′                                                                                              ⊗                                              u                                                  m                          2                          ′                                                                                                                                ]                                      ,                            (                  Eq          .                                          ⁢          8                )                                                      W            ~                                              m              1                        ,                          m              1              ′                        ,                          m              2                        ,                          m              2              ′                                            (            3            )                          =                                            1                                                3                  ⁢                                                                          ⁢                  Q                                                      ⁡                          [                                                                                                                  v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        v                                                  m                          1                          ′                                                                    ⊗                                              u                                                  m                          2                          ′                                                                                                                                                                        v                                                  m                          1                          ′                                                                    ⊗                                              u                                                  m                          2                          ′                                                                                                                                                                                                        v                                                  m                          1                                                                    ⊗                                              u                                                  m                          2                                                                                                                                                                        v                                                  m                          1                          ′                                                                    ⊗                                              u                                                  m                          2                          ′                                                                                                                                                                        -                                                  v                                                      m                            1                            ′                                                                                              ⊗                                              u                                                  m                          2                          ′                                                                                                                                ]                                .                                    (                  Eq          .                                          ⁢          9                )            
For each Con fig value, the different possible values of i′2 and the associated values of (s1, s2) and (p1,p2) corresponding to the rank-3 class A codebook are given in Table 2.
TABLE 2Selection of i2′ , (s1, s2), and (p1, p2) for Rank-3 Class A CodebookConfigSelected i2′ indices(s1, s2)(p1, p2)10, 2(1, 1)(−, −) 20-7, 16-23(O1, O2)  (                    O        1            2        ,                  O        2            2        ) 30-3, 8-11, 20- 23, 28-31(O1, O2)  (                    O        1            4        ,                  O        2            2        ) 40-15  (            O      1        ,                  O        2            2        )  (                    O        1            4        ,    -    )Rank-4 Class A Codebook
The rank-4 codebook can be defined in terms of four parameters: i1,1, i1,2, k and i′2. The different parameter values of parameter k represent different orthogonal beam groups. Each beam group consists of L′1 beams in the first dimension and L′2 beams in the second dimension, where (L′1,L′2) are defined in Eq. 3. During feedback, the UE feeds back k as part of the W1 indication. Each k value corresponds to one pair of (δ1,δ2) parameters as shown in Table 1. There can be two alternatives for the maximum value of k:                Alt 1. Two values: k=0,1 in Table 1        Alt 2. Maximum eight values:                    If N1>1 and N2>1: k=0, 1, 2 . . . , 7 in Table 1            If N2=1:k=0, 1, 2 in Table 1                        
Furthermore, i1,1 and i1,2, are defined as:                i1,1=0, 1, . . . , O1N1/s1−1        i1,2=0, 1, . . . , O2N2/s2−1        
Then, the rank-4 codebook can be defined as shown in the table shown in FIG. 20. In the table shown in FIG. 20, which shows a Rank 4 Class A Codebook, the rank-4 codewords Wm1,m1′,m2m2′,n(4) indexed by i′2 are defined as:
                    ⁢          (              Eq        .                                  ⁢        10            )                  W                        m          1                ,                  m          1          ′                ,                  m          2                ,                  m          2          ′                ,        n                    (        4        )              =                            1                                    4              ⁢                                                          ⁢              Q                                      ⁡                  [                                                                                          v                                          m                      1                                                        ⊗                                      u                                          m                      2                                                                                                                                        v                                          m                      1                      ′                                                        ⊗                                      u                                          m                      2                      ′                                                                                                                                        v                                          m                      1                                                        ⊗                                      u                                          m                      2                                                                                                                                        v                                          m                      1                      ′                                                        ⊗                                      u                                          m                      2                      ′                                                                                                                                                                φ                    n                                    ⁢                                                            v                                              m                        1                                                              ⊗                                          u                                              m                        2                                                                                                                                                              φ                    n                                    ⁢                                                            v                                              m                        1                        ′                                                              ⊗                                          u                                              m                        2                        ′                                                                                                                                                              -                                          φ                      n                                                        ⁢                                                            v                                              m                        1                                                              ⊗                                          u                                              m                        2                                                                                                                                                              -                                          φ                      n                                                        ⁢                                                            v                                              m                        1                        ′                                                              ⊗                                          u                                              m                        2                        ′                                                                                                                          ]                    .      
For each Config value, the different possible values of i′2 and the associated values of (s1, s2) and (p1,p2) corresponding to the rank-4 class A codebook are given in Table 3.
TABLE 3Selection of i2′, (s1, s2), and (p1, p2) for Rank-4 Class A CodebookConfigSelected i2′ indices(s1, s2)(p1, p2)10, 1(1, 1)(—, —) 20-3, 8-11(O1, O2)  (                    O        1            2        ,                  O        2            2        ) 30-1, 4-5, 10-11, 14-15(O1, O2)  (                    O        1            4        ,                  O        2            2        ) 40-7  (            O      1        ,                  O        2            2        )  (                    O        1            4        ,    -    )Ranks 5-8 Class A Codebooks
For ranks 5-8, the Class A codebooks are defined by two parameters: (i11, i12). The i1,1 and i1,2 parameters are defined as:                i1,1=0, 1, . . . , O1N1/s1−1        i1,2=0, 1, . . . , O2N2/s2−1For a given Config, (s1, s2) values are determined similar to Table 3. A precoding matrix codeword for rank r (r=5,6,7,8) is denoted as Wi1,1i1,2(r). The precoding matrix codewords Wi1,1i1,2(r), r=5,6,7,8 are then defined as in Equations 11-14, illustrated in FIG. 21 and FIG. 22.        
For sixteen ports (i.e., N1N2=8), the terms δ1,1, δ1,2, δ1,3, δ2,1, δ2,2, δ2,3 in Equations 11-14 are defined as in Table 4. For twelve ports (i.e., N1N2=6), the terms δ1,1, δ1,2, δ1,3, δ2,1, δ2,2, δ2,3 in Equations 11-14 are defined as in Table 5.
TABLE 4Delta values for cases with 16 ports and ranks 5-8Antennaconfigurationδ1,1δ2,1δ1,2δ2,2δ1,3δ2,3Config = 4N1 ≥ N2O102O103O10N1 < N20O202O203O2Config = 3N1 ≥ N2O102O1O23O1O2N1 < N20O2O12O2O13O2Config = 2BothO10O1O20O2
TABLE 5Delta values for cases with 12 ports and ranks 5-8TypeConfigurationδ1,1δ2,1δ1,2δ2,2δ1,3δ2,3Config = 4N1 ≥ N2O102O100O2N1 < N20O202O2O10Config = 3N1 ≥ N2O10O1O22O1O2N1 < N20O2O1O2O12O2Config = 2BothO10O1O20O2Codebook Subset Restriction
Codebook subset restriction (CSR) is supported in LTE, as of Release 12 of the 3GPP specifications, and is described in 3GPP TS 36.213 V12.3.0 and 3GPP TS 36.331 V12.3.0. With codebook subset restriction, a subset of the precoders in the codebook is restricted so that the UE has a smaller set of possible precoders to choose from. This effectively reduces the size of the codebook implying that the search for the best PMI can be done on the smaller unrestricted set of precoders, thereby also reducing the UE computational requirements for this particular search. Typically, the eNodeB would signal the codebook subset restriction to the UE by means of a bitmap in a dedicated message part of the AntennaInfo information element, one bit for each precoder in the codebook, where a 1 indicates that the precoder is restricted, meaning that the UE is not allowed to choose and report the precoder. Thus, for a codebook with Ac different codewords across all ranks, a bitmap of length Ac would be used to signal the codebook subset restriction. The number of bits Ac associated with different codebooks for different transmission modes is shown in Table 6 below. This allows for full flexibility for the eNodeB to restrict every possible subset of the codebook. There are thus 2Ac possible codebook subset restriction configurations. For large antenna arrays with many antenna elements, the effective beams become narrow and a codebook containing many precoders is required for the intended coverage area. Furthermore, for two-dimensional antenna arrays, the codebook size increases quadratically since the precoders in the codebook need to span two dimensions, typically the horizontal and vertical domain. Thus, the codebook size, i.e. the total number of possible precoding matrices W, can be very large. Signaling a codebook subset restriction in the LTE pre-release-13 way, by means of a bitmap with one bit for every precoder, can thus impose a large overhead, especially if the codebook subset restriction (CSR) is frequently updated or if there are many users served by the cell where each UE has to receive the CSR.
TABLE 6Number of bits in codebook subset restriction bitmap for applicabletransmission modesNumber of bits Ac2antenna8 antennaports4 antenna portsportsTransmission2 4mode 3Transmission664mode 4Transmission416mode 5Transmission416mode 6Transmission664 withmode 8alternativeCodeBookEnabledFor4TX-r12 = TRUE configured,otherwise 32Transmission696 with109modes 9alternativeCodeBookEnabledFor4TX-and 10r12 = TRUE configured,otherwise 64
To address the shortcomings of the legacy CSR, two-dimensional beam-based codebook subset restriction will be implemented in LTE Rel-13. Let (l1,l2) denote the two-dimensional beam in X1⊗X2 corresponding to the l1th DFT vector in the first dimension, e.g., horizontal dimension, and l2th DFT vector in the second dimension, e.g., vertical dimension. Then, codebook subset restriction (CSR) is supported for FD-MIMO, where:                CSR is configured via RRC signaling        A subset of two-dimensional beams (l1,l2) are forbidden, i.e., not allowed to be reported according to the CSR configuration                    A forbidden two-dimensional beam is not allowed in reporting with any rank                        Rank restriction is also supported        CSR can be also applied to W2         Number of PMI bits does not vary according to restricted subset                    Note: Codebook subset restriction targets e.g. performance/capacity, as in Rel-8 to Rel-12                        
It has been further agreed that                For W1 CSR, a bitmap of (N1O1N2O2) bits indicates a two-dimensional-beams subset restriction; this bitmap is referred to as Beam-Subset-Restriction in the rest of this document.        an additional 8-bit bitmap indicates rank restriction; this bitmap is referred to as Rank-Restriction in the rest of this document.        and a RRC parameter for CSR on Class A i2 (i.e., W2) will be introduced; this parameter, which takes the form of another bitmap, will be referred to as i2-Subset-Restriction in the rest of this document.        